Temporal Bias in Admission Control: When Periodic Gating Preserves Logical Error Rates in Surface-Code CTMCs

Periodic admission control (AC) can change when accepted events occur within a cycle even when long-run averages (e.g. total accepted injections per unit time) are unchanged. This "temporal bias" matters whenever logical-flip risk is phase-dependent or when analysts condition on accepted events without correcting for exposure. We formalize an exposure-proportional null for phase-resolved logical flips and propose two lightweight diagnostics: (i) a Poisson sinusoid regression on log-risk with an exposure offset, and (ii) an exact window-enrichment test (binomial conditional on the total number of flips), with a scan-corrected [5] Monte Carlo p-value when the phase offset is unknown. Applied to a representative L=11 run (η=0.9, γ=0.002, period 10, 60 phase bins, T max =10 7) we record N = 466,947 accepted injections and Y = 87 logical-Z flips (p 0 ≈ 1.863 × 10 −4 per accepted injection) and find no evidence of phase modulation at current statistics (sinusoid p ≈ 0.466; scan-corrected window p ≈ 0.694). We summarize power benchmarks (e.g. ≳ 700 flips to rule out ≥ 30% peak/trough modulation) and recommend reporting rules that prevent spurious phase effects in gated simulations and hardware-aligned experiments.